package algorithm.problems.tree;

/**
 * Created by gouthamvidyapradhan on 09/03/2017.
 * Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.
 * <p>
 * According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”
 * <p>
 * _______6______
 * /              \
 * ___2__          ___8__
 * /      \        /      \
 * 0      _4       7       9
 * /  \
 * 3   5
 * For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.
 */

public class LowestCommonAncestorBST {
    class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }

    public static void main(String[] args) throws Exception {

    }

    private TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root == null) return null;

        if (p.val == root.val || q.val == root.val) return root;

        else if ((p.val < root.val && q.val > root.val) || (q.val < root.val && p.val > root.val))
            return root;

        else if (p.val < root.val && q.val < root.val)
            return lowestCommonAncestor(root.left, p, q);

        else
            return lowestCommonAncestor(root.right, p, q);
    }
}
